Solve sqrt{25}(30-8)div25*5^2(8x^2)

$$\sqrt{ 25 } (30-8) \div 25 \times { 5 }^{ 2 } (8 { x }^{ 2 } )$$

Evaluate

$$880x^{2}$$

Solution Steps

Calculate the square root of 25 and get 5.

$$\frac{5\left(30-8\right)}{25}\times 5^{2}\times 8x^{2}$$

Subtract 8 from 30 to get 22.

$$\frac{5\times 22}{25}\times 5^{2}\times 8x^{2}$$

Multiply 5 and 22 to get 110.

$$\frac{110}{25}\times 5^{2}\times 8x^{2}$$

Reduce the fraction \frac{110}{25} to lowest terms by extracting and canceling out 5.

$$\frac{22}{5}\times 5^{2}\times 8x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{22}{5}\times 25\times 8x^{2}$$

Multiply \frac{22}{5} and 25 to get 110.

$$110\times 8x^{2}$$

Multiply 110 and 8 to get 880.

$$880x^{2}$$

Differentiate w.r.t. x

$$1760x$$

Steps Using Definition of a Derivative

Calculate the square root of 25 and get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(30-8\right)}{25}\times 5^{2}\times 8x^{2})$$

Subtract 8 from 30 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 22}{25}\times 5^{2}\times 8x^{2})$$

Multiply 5 and 22 to get 110.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{110}{25}\times 5^{2}\times 8x^{2})$$

Reduce the fraction \frac{110}{25} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{22}{5}\times 5^{2}\times 8x^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{22}{5}\times 25\times 8x^{2})$$

Multiply \frac{22}{5} and 25 to get 110.

$$\frac{\mathrm{d}}{\mathrm{d}x}(110\times 8x^{2})$$

Multiply 110 and 8 to get 880.

$$\frac{\mathrm{d}}{\mathrm{d}x}(880x^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 880x^{2-1}$$

Multiply 2 times 880.

$$1760x^{2-1}$$

Subtract 1 from 2.

$$1760x^{1}$$

For any term t, t^{1}=t.

$$1760x$$